• Korean Journal of Mathematics
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• v.23 no.3
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• pp.357-370
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• 2015

In this paper, we introduce the concept of (m, n)-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of (m, n)-ideals in an ordered semigroup [14]. We also study the (m, n)-regular class of an ordered AG-groupoid in terms of (m, n)-ideals.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.927-938
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• 2011

Let G be an abelian monoid with identity e. Let R be a G-graded commutative ring, and M a graded R-module. In this paper we first introduce the concept of graded primal submodules of M an give some basic results concerning this class of submodules. Then we characterize the graded primal ideals of the idealization R(+)M.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.9 no.6
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• pp.546-552
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• 2016

We present a quantitative evaluation of an algorithm for model-based face recognition. The algorithm actively learns how individual faces vary through video sequences, providing on-line suppression of confounding factors such as expression, lighting and pose. By actively decoupling sources of image variation, the algorithm provides a framework in which identity evidence can be integrated over a sequence. We demonstrate that face recognition can be considerably improved by the analysis of video sequences. The method presented is widely applicable in many multi-class interpretation problems.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.93-97
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• 1994

Previously T.Porter [3] has given a relative Chinese Remainder Theorem under the hypothesis that given ring R has at least one .tau.-closed maximal ideal (by his notation Ma $x_{\tau}$(R).neq..phi.). In this short paper we drop his overall hypothesis that Ma $x_{\tau}$(R).neq..phi. and give the proof and some related results with this Theorem. In this paper R will always denote a commutative ring with identity element and all modules will be unitary left R-modules unless otherwise specified. Let .tau. be a given hereditarty torsion theory for left R-module category R-Mod. The class of all .tau.-torsion left R-modules, dented by J is closed under homomorphic images, submodules, direct sums and extensions. And the class of all .tau.-torsionfree left R-modules, denoted by F, is closed under taking submodules, injective hulls, direct products, and isomorphic copies ([2], Proposition 1.7 and 1.10).

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.81-87
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• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.141-154
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• 2022

Let R be a commutative ring with identity. Denote by w𝒫_w the class of weak w-projective R-modules and by w𝒫_w^⊥ the right orthogonal complement of w𝒫_w. It is shown that (w𝒫_w, w𝒫_w^⊥) is a hereditary and complete cotorsion theory, and so every R-module has a special weak w-projective precover. We also give some necessary and sufficient conditions for weak w-projective modules to be w-projective. Finally it is shown that when we discuss the existence of a weak w-projective cover of a module, it is enough to consider the w-envelope of the module.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.717-734
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• 2024

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of weakly (m, n)-prime ideals generalizing (m, n)-prime and weakly (m, n)-closed ideals. A proper ideal I of R is called weakly (m, n)-prime if for a, b ∈ R, 0 ≠ a^mb ∈ I implies either aⁿ ∈ I or b ∈ I. We justify several properties and characterizations of weakly (m, n)-prime ideals with many supporting examples. Furthermore, we investigate weakly (m, n)-prime ideals under various contexts of constructions such as direct products, localizations and homomorphic images. Finally, we discuss the behaviour of this class of ideals in idealization and amalgamated rings.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.8 no.9
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• pp.563-571
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• 2018

The purpose of this study is to explore the direction of multicultural mentoring class activities in order to promote the professional growth and critical reflection of student mentors who are undergraduate students from a variety of major. For this purpose, the contents and phenomena of the multicultural mentoring of the mentor - mentee were reported as activity texts, and then seven directions of textuality were applied to explore the direction of multicultural mentoring class activities. As a result, coherence refers to the relationship between the mentor and the mentee for continuing the activities of multicultural mentoring, and cohesiveness refers to the relationship between the mentor and the mentee. It was called the achievement of identity. Intention means that the mentor has an intention or goal for the class before the mentoring activity, and tolerance means that the text produced by the mentor in the multicultural mentoring process is accepted by the mentee. Intentional means that the mentor has intention or goal for the class before the mentoring class activity, and tolerance means having the text as the class activity text when the mentor's text is accepted by the multicultural mentoring class activity process. In the case of informativeness, the information produced by the mentor is less informative when the mentee is predictable and less informative when the predictor is low. In the case of contextuality, contextuality of class activities can be changed according to the physical text situation and the mentee situation in class activity. In case of multicultural mentoring class activity, except for case where mentor creates new class activity text, it is related to the production of class activity texts through mentor learning experiences, peer friends' advice, and education.

• Journal of architectural history
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• v.16 no.1
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• pp.49-68
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• 2007

The purpose of this study is analysis of traditional noble houses style of Ha-Dong area in Kyeong-Nam. The sequence of this study is at first finding the list of survey object, and investigating of those houses, after than drawing the site and floor plan, and lately analysis the characters of inner and outer space of them. It required six months. The results of analysis of them are as follows. 1. The noble traditional houses in Ha-Dong are found eight samples which are not noticed in academic society. 2. The constructions of noble housing in late Period of Cho-sun Dynasty are divided in three parts as a general role. Its grade is similar in Ha-Dong. The number of traditional noble house of (old) volunteer class is two cases. The (new) rich-farmer class is four cases. And there are two cases of (long) authority class. 3. The type of site plan is based on Korean south area style which is the style of departed rectangular type. But outdoor spaces are divided in several space by many fence than other area. It is the special item of construction. 4. The special character of indoor space is the use of 'Gong-ru'. It is called similar space used in top of main entrance building of large building. But it is located in various space in Ha-dong. It is included in any space of Sarang-Che, An-Che, Are-Che. The traditional noble houses of Ha-Dong area have special spacial characters. For long time there space was developed based on local identity. And its characters was divided various classes. Thus Ha-Dong area is definite place of useful identified traditional culture.